Abstract: Infectious diseases pose a persistent threat to global health. This research leverages mathematical modeling as a critical tool to decipher the complex dynamics of disease transmission and to design effective intervention strategies. Focusing on case studies such as Plague, Polio, and Covid-19, I develop and fit models to real-world data to simulate outbreaks and quantitatively assess the impact of public health measures like vaccination and social distancing. A core component of my work involves rigorous model validation and stability analysis to ensure robust, reliable predictions of long-term outbreak behavior. The ultimate goal of this research is to generate actionable insights that inform public health policy and contribute to controlling the spread of infectious diseases.